Question: Jessica is 2 times as old as William. 25 years ago, Jessica was 7 times as old as William. How old is William now?
Solution: We can use the given information to write down two equations that describe the ages of Jessica and William. Let Jessica's current age be $j$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $j = 2w$ 25 years ago, Jessica was $j - 25$ years old, and William was $w - 25$ years old. The information in the second sentence can be expressed in the following equation: $j - 25 = 7(w - 25)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = 2w$ . Substituting this into our second equation, we get: $2w$ $-$ $25 = 7(w - 25)$ which combines the information about $w$ from both of our original equations. Simplifying the right side of this equation, we get: $2 w - 25 = 7 w - 175$ Solving for $w$ , we get: $5 w = 150.$ $w = 30$.